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# TP%235_f08 - CE 3102 Thought Problem 5 Introducing Random...

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CE 3102 Thought Problem 5 Introducing Random Variables Two types of vehicles use a road, passenger cars and trucks. Observations have indicated that, over a 2-minute interval, the different frequencies of trucks and passenger cars occur with the following probabilities: # Passenger Cars= 0 1 2 3 4 0 .03 .09 .09 .06 .03 1 .05 .15 .15 .1 .05 # Trucks= 2 .02 .06 .06 .04 .02 However, a road-tube traffic counter placed on this road is not able to distinguish between truck and passenger cars, but only counts total vehicles crossing in a 2-minute interval. (a) Characterize the set of outcomes which the tube counter could record, and determine the associated probability mass function (pmf) and cumulative distribution function (cdf). (b) What is the expected value and variance of this random variable?

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CE 3102 Fall 2008 Thought Problem 5 Instructor’s Partial Solution (a) The underlying sample space consists of combinations of truck and passenger car frequencies, which we can denote as ordered pairs (t,p), where t=truck count, and p=passenger car count. The function x(.) , denoting the total count, is then formed by simply adding the truck and passenger car frequencies, x(t,p) = t+p If we now let X denote the random variable giving the number of vehicles crossing in a
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• Spring '11
• Probability theory, probability density function, Cumulative distribution function, 2-minute interval, passenger car frequencies

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TP%235_f08 - CE 3102 Thought Problem 5 Introducing Random...

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